We give a speciic product decomposition of the base-point path connected component of the triple loop space of the suspension of the projective plane.

We give a specific product decomposition of the base-point path connected component of the triple loop space of the suspension of the projective plane.

Let X be a projective variety, homogeneous under a linear algebraic group. We show that the diagonal of X belongs to a unique irreducible component

Let $mathcal {A}$ be an abelian category with enough projective objects and $mathcal {X}$ be a full subcategory of $mathcal {A}$. We define Gorenstein projective objects with respect to $mathcal {X}$ and $mathcal{Y}_{mathcal{X}}$, respectively, where $mathcal{Y}_{mathcal{X}}$=${ Yin Ch(mathcal {A})| Y$ is acyclic and $Z_{n}Yinmathcal{X}}$. We point out that under certain hypotheses, these two G...

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

Let P (S) be the space of projective structures on a closed surface S of genus g > 1 and let Q(S) be the subset of P (S) of projective structures with quasifuchsian holonomy. It is known that Q(S) consists of infinitely many connected components. In this paper, we will show that the closure of any exotic component of Q(S) is not a topological manifold with boundary and that any two components o...

These notes form a rough outline of the correspondence between the PSL4(R)Hitchin component and convex foliated projective structures from [3].

In this paper $S$ is a monoid with a left zero and $A_S$ (or $A$) is a unitary right $S$-act. It is shown that a monoid $S$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $S$-act is quasi-projective. Also it is shown that if every right $S$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...

We express the genus-one degree-d GW-invariant of a projective complete intersection threefold in terms of the genus-zero degree-d GW-invariant and the integral of a natural class on the main component of the moduli space of genus-one degree-d stable maps into the corresponding projective space P. This integral is computable via the classical localization theorem. The method described in this p...